Effects of Time-Dependent Edge Dynamics on Properties of Cumulative Networks

Abstract — Inspecting the dynamics of networks opens a new dimension in understanding the interactions among the components of complex systems. Our goal is to understand the baseline properties to be expected from elementary random changes over time, in order to be able to assess the effects found in longitudinal data.In our earlier work, we created elementary dynamic models from classic random and preferential networks. Focusing on edge dynamics, we defined several processes changing networks of fixed size. We applied simple rules, including random, preferential or assortative modification of existing edges - or a combination of these. Starting from initial Erdos-Renyi or Barabasi-Albert networks, we examined various basic network properties (e.g., density, clustering, average path length, number of components, degree distribution, etc.) of both snapshot and cumulative networks (of various lengths of aggregation time windows). In the current paper, we extend this line of research by applying time-dependent edge creation and deletion algorithms. I.e., we model processes where edge dynamics is defined as a function of time.Our results provide a baseline for changes to be expected in dynamic networks. Also, they suggest that certain network properties have a strong, non-trivial dependence on the length of the sampling window.

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FurtherMotivations<br />Incertaindomains (e.g., inchemicalreactions) interactionsareforshorttimeonly<br />Human interactionsarealsotemporal<br /> „(…), the very behavior that makes these people important tovaccinate can help us finding them. People you have met recently are more likely to be socially active andthus central in the contact pattern, and important to vaccinate. We propose two immunization schemesexploiting temporal contact patterns.”<br /> (S .Lee, L.E.C. Rocha, F.Liljeros, P.Holme. Exploiting temporal networkstructures of human interaction to effectively immunize population. arXiv:q-bio/1011.3928, 2010.)<br />